1. Field of the Invention
The present invention relates to an image forming apparatus, such as electrophotographic printers, ionographic printers, ink-jet printers, or facsimiles, and more particularly to a drive technique suitable for use with tandem color copiers or color printers which employ a plurality of drum-like image forming members.
2. Description of the Related Art
Like electrophotographic printers, an apparatus which produces an image on recording paper is usually provided with an image forming member. An electrostatic latent image is formed on the surface of the image forming member while the image forming member is rotating, and the thus-formed latent image is developed by means of toner to thereby produce a developed image. In order to drive the image forming member in a rotating manner, the image forming apparatus is usually provided with a mechanism to transmit driving force to a drive shaft of the image forming member from a motor via a deceleration mechanism such as a gear or a timing belt so that the image forming member is rotated at a constant speed.
However, as can be seen from a schematic representation of a deceleration mechanism which employs gears shown in FIG. 29, in a case where a drive mechanism for use with the image forming member is constituted by interposing a deceleration gear unit which employs a combination of a plurality of gears 502 and 503 between a drive shaft 1a of the image forming member 1 and a motor 501, there will arise mechanical errors such as an offset "d" or meshing errors. As a result, variations as shown in FIG. 30 arise. Further, variations due to the offset of a pulley arise in the rotation of the rotation transmission mechanism that employs the timing belt. As described above, in the case of the conventional drive mechanism, variations arise in the rotational speed of the image forming member, which in turn pauses a problem for formation of a toner image.
This problem arises in the form of inconsistencies in density of an image for monochrome copiers or printers as well as in the form of imperfect images, such as variations in color or streaks of color, for color copiers or printers. For these reasons, it is desired to reduce variations in the rotational speed to as small an amount as possible, and consequently there has been a demand for a higher degree of accuracy of machining and assembly of the members of the drive mechanism.
However higher the accuracy of the drive mechanism may be improved, variations arise in the rotational speed of the image forming member, if the shaft of the motor or of the image forming member has an offset, or if the image forming member itself has an offset.
Japanese Patent Application Laid-open No. Hei-7-140844 discloses a sensing and controlling method as means for solving the foregoing problem. This method enables sensing and controlling of variations in the rotational speed of each of motors respectively attached to a plurality of image forming members by means of speed sensing means fitted to the drive shaft of each image forming member.
There is another known method in which positional information about image data to be finally output is sensed, and amendments are made to the timing at which an optical signal is output or to the trail of an optical axis. Japanese Patent Application Laid-open No. Hei-6-79917 discloses a method in which the displacements of toner on a transfer drum are sensed, and address offset data for each scanning line of a write beam is calculated from the result of the sensing operation and is then stored. The address of the write beam is corrected in the primary and secondary scanning directions.
Since the previously-described methods result in an increase in the size of the image forming apparatus or a significant increase in the cost, it is considerably difficult to apply the methods to inexpensive compact image forming apparatuses. Further, the methods suffer their insufficient versatility.
For example, Japanese Patent Application Laid-open No. Hei-7-319254 discloses a method in which an endless flat belt which is single transmission-and-drive means is brought into contact with the outer peripheral surface of a plurality of image forming members, and a rotational drive force is transmitted to a plurality of photosensitive drums by means of the frictional force developing between the outer peripheral surface of the photosensitive drums and the endless flat belt, whereby the outer peripheral surface of each of the photosensitive drums is actuated to the same extent.
Japanese Patent Application Laid-open No. Sho-62-55674 discloses a method intended for actuating each of a plurality of image forming members and a sheet conveyor belt to the same extent. By this method, the image forming members and the sheet conveyor/transfer belt are actuated in association with each other through use of a transmission member driven by a single drive source.
In both the previously-described existing methods disclosed in Japanese Patent Application Laid-open Nos. Hei-7-319254 and Sho-62-55674, exciting means, such as gears, which cause transmission of vibration are removed from a drive force transmission mechanism. Consequently, they are superior with regard to the reduction in the exciting components developing in the tooth bearings of the gears; and the prevention of variations in the rotation of the gear due to the exciting components and streaks of inconsistencies in color or density in a high frequency range.
As the reduction in the size and cost of the image forming apparatus has been improving in recent years in accordance with market demands, the image forming members and transmission members are also reduced in diameter. Accordingly, the number of rotations of these members is increasing. Further, in accordance with the increase in the number of rotations, variations in the rotation of the image forming member or transmission member due to the offset of the constituent elements are gradually increasing from a low frequency range to a higher frequency range. The pitch of variations-in-color resulting from the variations-in-rotation also becomes smaller, resulting in a tendency for the variations-in-color to become easily visually recognizable. For example, in the case of an existing image forming member having a diameter of 84 mm, if one variation arises in the image forming member every rotation, this variation appears in the form of a variation-in-color with a pitch of 84.times..pi.=264 mm; namely, in the form of a considerably mild variation. If the diameter is as small as 20 mm or 15 mm; particularly, if the diameter is 15 mm, the pitch of the variation-in-color becomes as narrow as 15.times..pi.=47 mm, thereby resulting in the variation-in-color being visually recognizable. Therefore, if consideration is given to the reduction in the size and cost of the image forming apparatus, a solution to variable components due to the offset of the image forming member presents a problem.
Neither the method disclosed in JP-A Laid-open No. Hei-7-319254 or the method disclosed in JP-A Laid-open No. Sho-62-55674 has means for removing the offset of the image forming member due to the positional offset or inclination of the support shaft of the image forming member. Consequently, in the methods disclosed in the foregoing Japanese Patent Applications, even if each image forming member is maintained at a constant rotational speed, the surface velocity of each image forming member at the position where a latent image is formed varies from image forming member to image forming member because of the offset of the image forming member with respect to its rotational center. Resultant color images are displaced from each other by an image transfer section when the image is transferred.
Elements in the variation in speed of the drive force transmission system from the drive source to the surface of the image forming member will be described.
FIG. 31 shows a schematic representation of an existing drive force transmission system.
In a case where the image forming apparatus has the drive force transmission system as shown in FIG. 31, the way the surface velocity V.sub.PR of the image forming member changes will be induced by Formula.
Assuming that a variation in each element is considered to be analogously represented by a sine vibration, and that disc-shaped flanges are attached to the rotational shaft of the image forming member. Further, assuming that a pipe-shaped photosensitive drum having a predetermined thickness t.sub.PR (mm) is fixed in such a way that the outer periphery of the flange comes into contact with the internal peripheral surface of the photosensitive drum.
Hereinafter, the amplitude of variation is A.sub.i, the frequency of variation is f.sub.i, and the phase of variation is .PHI..sub.i (suffix i designates each element).
First, with regard to the variation in a motor, assuming that a mean angular velocity is .omega..sub.m0 rad/sec!, the angular velocity .omega..sub.m of the motor rad/sec! is given by EQU .omega..sub.m =.omega..sub.m0 (1+A.sub.1 sin(2.pi.f.sub.1 t+.PHI..sub.1))(1 )
Assuming that a mean radius of the motor shaft is r.sub.m0 (mm), the radius of the motor shaft r.sub.m (mm) is given by EQU r.sub.m =r.sub.m0 (1+A.sub.2 sin(2.pi.f.sub.2 t+.omega..sub.2))(2)
Consideration will now be given to a deceleration apparatus. Here, assuming the reduction rate of two-stage deceleration of gears.
Reduction rate: r.sub.r is given by EQU r.sub.r =(r.sub.g1 /r.sub.m).times.(r.sub.g3 /r.sub.g2) (3)
Assuming the mean radii of the respective deceleration means are r.sub.g10, r.sub.g20, r.sub.g30 (mm), the radii r.sub.g1, r.sub.g2, r.sub.g3 (mm) are given by EQU r.sub.g1 =r.sub.g10 (1+A.sub.3 sin((2.pi.f.sub.3 t+.PHI..sub.3))(4) EQU r.sub.g2 =r.sub.g20 (1+A.sub.4 sin((2.pi.f.sub.4 t+.PHI..sub.4))(5) EQU r.sub.g3 =r.sub.g30 (1+A.sub.5 sin((2.pi.f.sub.5 t+.PHI..sub.5))(6)
With regard to the image forming member, the radius r.sub.s (mm) of the rotary shaft of the image forming member is given by EQU r.sub.s =r.sub.s0 (1+A.sub.6 sin((2.pi.f.sub.6 t+.PHI..sub.6))(7)
Assuming that the mean distance between the inner shaft of the flange to the outer periphery of the flange is d.sub.f0 (mm), a distance d.sub.f (mm) is given by EQU d.sub.f =d.sub.f0 (1+A.sub.7 sin((2.pi.f.sub.7 t+.PHI..sub.7))(8)
Assuming that the mean thickness of the cylindrical photosensitive drum which constitutes the image forming member is t.sub.PR0 (mm), a thickness t.sub.PR (mm) is given by EQU t.sub.PR =t.sub.PR0 (1+A.sub.8 sin((2.pi.f.sub.8 t+.PHI..sub.8))(9)
Assuming that the sum of the three elements described above is an effective radius, a surface velocity V.sub.PR (mm/sec) of the photosensitive drum is given by ##EQU1##
As represented by Formula (10'), the surface velocity V.sub.PR of the photosensitive material is represented by a dependent function of each constituent element. Each element in Formula (10') includes a variation whose amplitude A.sub.i and phase .PHI..sub.i are arbitrarily given by the Formulae (1) through (9), and hence the final surface velocity V.sub.PR of the image forming member varies to a considerably large extent.
There is a drive method in which a single element is used for the motor and the deceleration mechanism. More specifically, in a case where an image forming apparatus has four image forming members, a drive motor and a deceleration mechanism are commonly used by the four image forming members. If this method is used as means for preventing the previously-described variation in the surface velocity of the image forming member, variations in independent variables: .omega..sub.m, r.sub.m, r.sub.g1, r.sub.g2, and r.sub.g3 are brought in phase with each other with regard to the four image forming members. Accordingly, displacements of color which would be otherwise caused by variations in the variables can be prevented.
However, since the elements r.sub.s, d.sub.f and t.sub.PR have various values in each of an image forming member, they cannot be removed by the foregoing existing drive method.